A REINTERPRETATION OF THE FLOQUET SOLUTION OF THE ORDINARY DIFFERENTIAL EQUATION SYSTEM WITH PERIODIC COEFFICIENTS AS A PROBLEM OF AN INFINITE MATRIX

1986 ◽  
Vol 5 (1) ◽  
pp. 1-22 ◽  
Author(s):  
TADEUSZ SOBCZYK
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Equation System ◽  
Infinite Matrix ◽  
Differential Equation System ◽  
Periodic Coefficients ◽  
Floquet Solution ◽  
Ordinary Differential Equation System

scholarly journals Transient Dynamics in the Random Growth and Reset Model

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 306
Author(s):  
Tamás S. Biró ◽  
Lehel Csillag ◽  
Zoltán Néda
Keyword(s):  
Differential Equation ◽  
Mean Field ◽  
Equation System ◽  
Transient Dynamics ◽  
Type Model ◽  
Discrete Version ◽  
Differential Equation System ◽  
Practical Applications ◽  
Random Growth ◽  
Recursive Integration

A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches. The first method is based on mathematical induction by the recursive integration of the coupled differential equations for the discrete states. The second method transforms the coupled ordinary differential equation system into a partial differential equation for the generating function. We derive analytical results for some important, practically interesting cases and discuss the obtained results for the transient dynamics.

scholarly journals Kestabilan Model Epidemi SEIR Dengan Laju Insidensi

2015 ◽  
Vol 10 (2) ◽  
pp. 74
Author(s):  
Roni Tri Putra ◽  
Sukatik - ◽  
Sri Nita
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Equation System ◽  
Differential Equation System ◽  
Equilibrium Existence

In this paper, it will be studied stability for a SEIR epidemic model with infectious force in latent, infected and immune period with incidence rate. From the model it will be found investigated the existence and uniqueness solution  of points its equilibrium. Existence solution of points equilibrium proved by show its differential equations system of equilibrium continue, and uniqueness solution of points equilibrium proved by show its differential equation system of equilibrium differentiable continue. 

scholarly journals An accelerated differential equation system for generalized equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Qiyuan Wei ◽  
Liwei Zhang
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Maximal Monotone ◽  
Equation System ◽  
Generalized Equation ◽  
Generalized Equations ◽  
Differential Equation System ◽  
Step Size ◽  
Yosida Regularization ◽  
Numerical Discretization

<p style='text-indent:20px;'>An accelerated differential equation system with Yosida regularization and its numerical discretized scheme, for solving solutions to a generalized equation, are investigated. Given a maximal monotone operator <inline-formula><tex-math id="M1">\begin{document}$ T $\end{document}</tex-math></inline-formula> on a Hilbert space, this paper will study the asymptotic behavior of the solution trajectories of the differential equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation} \dot{x}(t)+T_{\lambda(t)}(x(t)-\alpha(t)T_{\lambda(t)}(x(t))) = 0,\quad t\geq t_0\geq 0, \end{equation} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>to the solution set <inline-formula><tex-math id="M2">\begin{document}$ T^{-1}(0) $\end{document}</tex-math></inline-formula> of a generalized equation <inline-formula><tex-math id="M3">\begin{document}$ 0 \in T(x) $\end{document}</tex-math></inline-formula>. With smart choices of parameters <inline-formula><tex-math id="M4">\begin{document}$ \lambda(t) $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}$ \alpha(t) $\end{document}</tex-math></inline-formula>, we prove the weak convergence of the trajectory to some point of <inline-formula><tex-math id="M6">\begin{document}$ T^{-1}(0) $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M7">\begin{document}$ \|\dot{x}(t)\|\leq {\rm O}(1/t) $\end{document}</tex-math></inline-formula> as <inline-formula><tex-math id="M8">\begin{document}$ t\rightarrow +\infty $\end{document}</tex-math></inline-formula>. Interestingly, under the upper Lipshitzian condition, strong convergence and faster convergence can be obtained. For numerical discretization of the system, the uniform convergence of the Euler approximate trajectory <inline-formula><tex-math id="M9">\begin{document}$ x^{h}(t) \rightarrow x(t) $\end{document}</tex-math></inline-formula> on interval <inline-formula><tex-math id="M10">\begin{document}$ [0,+\infty) $\end{document}</tex-math></inline-formula> is demonstrated when the step size <inline-formula><tex-math id="M11">\begin{document}$ h \rightarrow 0 $\end{document}</tex-math></inline-formula>.</p>

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